We've had some doozies.
One we called Mr. Smiley. He lived alone. He'd look up if you said hello, but would just frown and would never respond. I never saw him leave the house except to pick up his newspaper or to "jog" in his backyard. He did laps around the small back in really tight spandex shorts, a red headband and no shirt. It was the funniest outfit. He had little bird legs and was very wrinkled and he just circled around and around.
Then there was the couple who weren't married. She used to call the police when they'd fight, but refused to ever press charges.

Maybe he was really abusive, but most of the times I saw them they were in a liplock, so I think it was just a rocky relationship. I got pulled into one of the disputes when she beat on my door claiming he was going to kill her. When the police arrived she had calmed down and wanted to go back home.
Then we moved across town. The family behind us was incredible. The kids ran loose and did whatever they wanted. They used to shoot at the street lights with their BB guns and shot out three of our windows. One night one of the boys locked mom and dad out of the house and smashed up every room in the house with a baseball bat while they were trying to get inside. We were relieved when they moved away, but the new owners had to redo the whole house.
Our next door neighbors let their young teen sons and their buddies play tag on the highly sloped roof. Their roof is just like ours and my DH is nervous when he has to get up on ours. It's hard to keep your footing. The kids run and skid and slide to the edge. I know the parents know they are up there...they have to be able to hear it inside. I'd be scared to death that one would slip and fall off the roof and break his neck. Maybe they figure one less mouth to feed? But I'd also be scared that I'd get sued if a neighbor kid fell.
We have an older couple down the street that prefers to sit in the garage on lawn chairs. And if the family comes to visit they pull out more chairs and still sit in the garage. I know they have a lovely yard, so I always wonder why they choose to sit in the garage.
Our other next door neighbors like to do archery. They shoot at our privacy fence and often overshoot. We find enough arrows in the back that sometimes I wonder if the native americans are attacking. DH has told them repeatedly that we have dogs and would prefer they point another direction, but they persist.
Oh and we also used to have a scissor-snipper. He cut his grass several times a week and snipped almost daily. I know our yard drove him batty because DH only cuts ours once a week and trims the same.
My favorite neighbor by far is the little guy two doors down. He comes to visit regularly and always tells the most outlandish tall tale. We love it when he comes. Our favorite was when he told us about his dog (imaginary because we know his brother is deathly afraid of dogs). Said imaginary dog died, I won't go into the whole story, and when he told it he said in a very dramatic voice "and then we noticed our dog was dead.....dead, dead, DEAD! So now we always joke about things being dead, dead, DEAD! I feel sure his parents would be mortified at the stories he tells us, so we keep them to ourselves.